To create realistic looking textures without photosourcing, most of the texture has to be painted manually. Now, I will roughly explain how to do so.
Add a Background layer with a background colour which is sort of an average of the colours the actual animal will have. Paste the UV of your animal and make it a Multiplication or Burn Layer. This can be disabled for saving, so you don't have the grid on the texture, but you can see it while painting.
Add a new layer above the background and paint the basic colours of your animal.
Add a Soft Light layer and give it some generic noisy texture, usually some leather stuff.
Add various Texture layers, all Soft Light, to add some variability in the texture.
Paint finer details into a new layer.
Use a Soft light layer to paint general shade, using black.
Use another Soft light layer to paint highlights using white.